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SECTION – I (Total Marks : 24)
(Single Correct Answer Type)
This Section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONLY ONE is correct.
Q. Which of the field patterns given below is valid for electric field as well as for magnetic field?
A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The velocity V of the bullet is
v_{ball} = 20 m/s
v_{bullet} = 100 m/s
0.01 V = 0.01 x 100 + 0.2 x 20
v = 100 + 400 = 500 m/s
The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with
a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the
main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a
relative error of 2 %, the relative percentage error in the density is
A wooden block performs SHM on a frictionless surface with frequency, ν_{0}. The block carries a charge +Q on its surface. If now a uniform electric field is switchedon as shown, then the SHM of the block will be
A light ray travelling in glass medium is incident on glassair interface at an angle of incidence θ. The reflected (R) and transmitted (T) intensities, both as function of θ, are plotted. The correct sketch is
After total internal reflection, there is no refracted ray.
A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is
ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its
ejection, the kinetic energy of the object is
A long insulated copper wire is closely wound as a spiral of ‘N’ turns. The spiral has inner radius ‘a’ and outer radius ‘b’. The spiral lies in the XY plane and a steady current ‘I’ flows through the wire. The Zcomponent of the magnetic field at the centre of the spiral is
A point mass is subjected to two simultaneous sinusoidal displacements in xdirection, x_{1}(t) = A sinωt and
Adding a third sinusoidal displacement x_{3}(t) = B sin (ωt + φ) brings the mass to a complete rest. The values of B and φ are
SECTION – II (Total Marks : 16)
(Multiple Correct Answer(s) Type)
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE OR MORE may be correct.
Q. Two solid spheres A and B of equal volumes but of different densities d_{A} and d_{B} are connected by a string. They are fully immersed in a fluid of density d_{F}. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if
A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision
During collision friction is impulsive and immediately after collision the ring will have a clockwise angular
velocity hence friction will be towards left.
Which of the following statement(s) is/are correct?
(D) is correct if we assume it is work done against electrostatic force
A series RC circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current I_{R} through the resistor and voltage V_{C} across the capacitor are compared in the two cases. Which of the following is/are true?
SECTIONIII (Total Marks : 24)
(Integer Answer Type)
This section contains 6 questions. The answer to each of the questions is a singledigit integer, ranging from 0 to 9.
Enter only the numerical value in the space provided below.
Q. A series RC combination is connected to an AC voltage of angular frequency ω = 500 radian/s. If the
impedance of the RC circuit is the time constant (in millisecond) of the circuit is
A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in freespace.
It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the
sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the
sphere is A x 10^{z }(where 1 < A < 10). The value of ‘Z’ is
A train is moving along a straight line with a constant acceleration ‘a’. A boy standing in the train throws a
ball forward with a speed of 10 m/s, at an angle of 60° to the horizontal. The boy has to move forward by
1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s^{2}, is
A block of mass 0.18 kg is attached to a spring of forceconstant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is unstretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block m/s is V = N/10. Then N is:
Let ν be the speed of the block just after impulse. At B, the block comes to rest.
Therefore: Loss in K.E. of the block = Gain in P.E. of the spring + Work done against friction
Two batteries of different emfs and different internal resistances are connected as shown. The voltage across AB in volts is
Water (with refractive index = 4/3 in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature ‘R = 6 cm’ as shown. Consider oil to act as a thin lens. An object ‘S’ is placed 24 cm above water surface. The location of its image is at ‘x’ cm above the bottom of the tank. Then ‘x’ is
V_{2} = 16 cm
x = 18  16 = 2 cm
(MatrixMatch Type)
This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II.
Q. One mole of a monatomic gas is taken through a cycle ABCDA as shown in the PV diagram. Column II give the characteristics involved in the cycle. Match them with each of the processes given in Column I.
Process A → B → Isobaric compression
Process B → C → Isochoric process
Process C → D → Isobaric expansion
Process D → A → Polytropic with TA = TD
Column I shows four systems, each of the same length L, for producing standing waves. The lowest
possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as
λ_{f}. Match each system with statements given in Column II describing the nature and wavelength of the
standing waves.
SECTION – I (Total Marks : 24)
(Single Correct Answer Type)
This Section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONLY ONE is correct.
Q. The freezing point (in ^{o}C) of a solution containing 0.1 g of K_{3}[Fe(CN)_{6} (Mol. Wt. 329) in 100 g of water
(K_{f} = 1.86 K kg mol^{1}) is
Amongst the compounds given, the one that would form a brilliant colored dye on treatment with NaNO_{2} in
dil. HCl followed by addition to an alkaline solution of βnaphthol is
The major product of the following reaction is
Oxidation states of the metal in the minerals haematite and magnetite, respectively, are
Haematite : Fe_{2}O_{3} : 2x + 3 × (2) = 0
x =3
Magnetite : Fe_{3}O_{4} [an equimolar mixture of FeO and Fe_{2}O_{3}]
FeO : x – 2 = 0 ⇒ x = 2
Fe_{2}O_{3} : x = 3
Among the following complexes (KP)
K_{3}[Fe(CN)_{6}] (K), [Co(NH_{3})_{6}]Cl_{3} (L), Na_{3}[Co(oxalate)_{3}] (M), [Ni(H_{2}O)_{6}]Cl_{2} (N), K_{2}[Pt(CN)_{4}] (O) and
[Zn(H_{2}O)_{6}](NO_{3})_{2} (P)
Passing H_{2}S gas into a mixture of Mn^{2+}, Ni^{2+}, Cu^{2+} and Hg^{2+} ions in an acidified aqueous solution precipitates
H_{2}S in presence of aqueous acidified solution precipitates as sulphide of Cu and Hg apart from Pb^{+2}, Bi^{+3}, Cd^{+2}, As^{+3}, Sb^{+3} and Sn^{+2}.
Consider the following cell reaction:
At [Fe^{2+}] = 10^{3} M, P(O_{2}) = 0.1 atm and pH = 3, the cell potential at 25^{o}C is
SECTION – II (Total Marks : 16)
(Multiple Correct Answer(s) Type)
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE OR MORE may be correct.
Q. Reduction of the metal centre in aqueous permanganate ion involves
In acidic medium
In neutral medium
Hence, number of electron loose in acidic and neutral medium 5 and 3 electrons respectively.
The correct functional group X and the reagent/reaction conditions Y in the following scheme are
Condensation polymers are formed by condensation of a diols or diamine with dicarboxylic acids.
For the first order reaction
2N_{2}O_{5}(g) → 4NO_{2}(g) + O_{2}(g)
For first order reaction
[A] = [A]_{0}e^{–kt}
Hence concentration of [NO_{2}] decreases exponentially.
Also, t_{1/2} =. Which is independent of concentration and t_{1/2} decreases with the increase of
temperature.
The equilibrium
in aqueous medium at 25^{o}C shifts towards the left in the presence of
Cu^{2+} ions will react with CN^{} and SCN^{} forming [Cu(CN)^{4}]^{3} and [Cu(SCN)^{4}]^{3} leading the reaction in the backward direction.
Cu^{2+} also combines with CuCl_{2} which reacts with Cu to produce CuCl pushing the reaction in the backward direction.
SECTIONIII (Total Marks : 24)
(Integer Answer Type)
This section contains 6 questions. The answer to each of the questions is a singledigit integer, ranging from 0 to 9.
Enter only the numerical value in the space provided below.
Q. The maximum number of isomers (including stereoisomers) that are possible on monochlorination of the
following compound is
Total = 2 + 4 + 1 + 1 = 8
The total number of contributing structure showing hyperconjugation (involving CH bonds) for the
following carbocation is
6 x Hatoms are there
Among the following, the number of compounds than can react with PCl_{5} to give POCl_{3} is O_{2}, CO_{2}, SO_{2}, H_{2}O, H_{2}SO_{4}, P_{4}O_{10}
The volume (in mL) of 0.1 M AgNO_{3} required for complete precipitation of chloride ions present in 30 mL
of 0.01 M solution of [Cr(H_{2}O)_{5}Cl]Cl_{2}, as silver chloride is close to
Number of ionisable Cl^{} in [Cr(H_{2}O)_{5}Cl]Cl_{2} is 2
Millimoles of Cl^{} = 30 x 0.01 ´ 2 = 0.6
Millimoles of Ag^{+} required = 0.6
0.6 = 0.1 V
V = 6 ml
In 1 L saturated solution of AgCl [K_{sp}(AgCl) = 1.6 x 10^{10}], 0.1 mol of CuCl [K_{sp}(CuCl) = 1.0 x 10^{6}] is
added. The resultant concentration of Ag+ in the solution is 1.6 x 10^{x}. The value of “x” is
The number of hexagonal faces that are present in a truncated octahedron is
SECTIONIV (Total Marks : 16)
(MatrixMatch Type)
This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II.
Q. Match the transformations in column I with appropriate options in column II
Match the reactions in column I with appropriate types of steps/reactive intermediate involved in these
reactions as given in column II
SECTION – I (Total Marks : 24)
(Single Correct Answer Type)
This Section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONLY ONE is correct.
Q. If
Let f : [1, 2] → [0, ∞) be a continuous function such that f(x) = f(1  x) for all x ε[1, 2]. Let and R_{2} be the area of the region bounded by y = f(x), x = 1, x = 2, and the xaxis. Then
Let f(x) = x^{2} and g(x) = sinx for all x ε R. Then the set of all x satisfying (f o g o g o f) (x) = (g o g o f) (x),
where (f o g) (x) = f(g(x)), is
(fogogof) (x) = sin^{2} (sin x^{2})
(gogof) (x) = sin (sin x^{2})
sin^{2} (sin x^{2}) = sin (sin x^{2})
⇒ sin (sin x^{2}) [sin (sin x^{2})  1] = 0
⇒ sin (sin x^{2}) = 0 or 1
⇒ sin x^{2} = nπ or 2mπ + π/2, where m, n ε I
⇒ sin x^{2} = 0
⇒ x^{2} = np x = ± np , n Î {0, 1, 2, …}.
Let (x, y) be any point on the parabola y^{2} = 4x. Let P be the point that divides the line segment from (0, 0)
to (x, y) in the ratio 1 : 3. Then the locus of P is
y^{2} = 4x and Q will lie on it
(4k)^{2} = 4 ´ 4h
k^{2} = h
y^{2} = x (replacing h by x and k by y)
Let P(6, 3) be a point on the hyperbola If the normal at the point P intersects the xaxis at (9,
0), then the eccentricity of the hyperbola is
A value of b for which the equations
x^{2} + bx  1 = 0
x^{2} + x + b = 0,
have one root in common is
x^{2} + bx  1 = 0
x^{2} + x + b = 0 … (1)
Common root is
(b  1) x  1  b = 0
Let ω =1 be a cube root of unity and S be the set of all nonsingular matrices of the form where each of a, b, and c is either ω or ω^{2}. Then the number of distinct matrices in the set S is
The circle passing through the point (1, 0) and touching the yaxis at (0, 2) also passes through the point
Circle touching yaxis at (0, 2) is (x  0)^{2} + (y  2)^{2} + λx = 0 passes through ( 1, 0)
1 + 4  λ = 0 ⇒ λ = 5
x^{2} + y^{2} + 5x  4y + 4 = 0
Put y = 0 ⇒ x =  1,  4
Circle passes through ( 4, 0)
SECTION – II (Total Marks : 16)
(Multiple Correct Answer(s) Type)
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE OR MORE may be correct.
Q.
Clearly, f (x) is not differentiable at x = 0 as f´(0^{}) = 0 and f´(0^{+}) = 1.
f (x) is differentiable at x = 1 as f' (1^{–}) = f'(1^{+}) = 1.
where be is a constant such that 0 < b < 1. Then
Let L be a normal to the parabola y^{2} = 4x. If L passes through the point (9, 6), then L is given by
y^{2} = 4x
Equation of normal is y = mx – 2m – m^{3}.
It passes through (9, 6)
⇒ m^{3} – 7m + 6 = 0
⇒ m = 1, 2, – 3
⇒ y – x + 3 = 0, y + 3x – 33 = 0, y – 2x + 12 = 0.
Let E and F be two independent events. The probability that exactly one of them occurs is and the
probability of none of them occurring is If P(T) denotes the probability of occurrence of the event T,
then
SECTIONIII (Total Marks : 24)
(Integer Answer Type)
This section contains 6 questions. The answer to each of the questions is a singledigit integer, ranging from 0 to 9.
Enter only the numerical value in the space provided below.
Q. Let be three given vectors. If and then the value of is
The straight line 2x  3y = 1 divides the circular region x2 + y2 < 6 into two parts. If
then the number of point(s) in S lying inside the smaller part is
Let ω = e^{iπ/3}, and a, b, c, x, y, z be nonzero complex numbers such that
a + b + c = x
a + bω + cω^{2} = y
a + bω^{2} + cω = z.
The expression may not attain integral value for all a, b, c
If we consider a = b = c, then
x = 3a
The number of distinct real roots of x^{4}  4x^{3} + 12x^{2} + x  1 = 0 is
Let f (x) = x^{4}  4x^{3} + 12x^{2} + x  1 = 0
f'(x) = 4x^{3}  12x^{2} + 24x + 1= 4 (x^{3}  3x^{2} + 6x) + 1
f''(x) = 12x^{2}  24x + 24 = 12 (x^{2}  2x + 2)
f''(x) has 0 real roots
f (x) has maximum 2 distinct real roots as f (0) = –1.
Let y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x ε R, where f'(x) denotes and g(x) is a given nonconstant
differentiable function on R with g(0) = g(2) = 0. Then the value of y(2) is
y'(x) + y(x) g'(x) = g(x) g'(x)
⇒ e^{g(x)} y'(x) + e^{g(x)} g'(x) y(x) = e^{g(x)} g(x) g'(x)
Let M be a 3 x 3 matrix satisfying
Then the sum of the diagonal entries of M is
SECTIONIV (Total Marks : 16)
(MatrixMatch Type)
This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II.
Q. Match the statements given in Column I with the values given in Column II
Match the statements given in Column I with the intervals/union of intervals given in Column II
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